Question

The figures below depict pairs of parallel lines. Write down the formula for the line whose graph goes through:

The origin in figure a
Point (0, 3) in figure b

Answer 1

a) The formula for the figure A is
`y = -x`, b) The formula for the figure B is
`y = -x +3`-

Explanation:

From Analytical Geometry, we know that two lines are parallel to each other when they share the same slope. We get the slope of figure B by means of the slope formula:

`m = (y_(2)-y_(1))/(x_(2)-x_(1))`

Where:

`x_(1)`,
`x_(2)` - Initial and final x-coordinates, dimensionless.

`y_(1)`,
`y_(2)` - Initial and final y-coordinates, dimensionless.

`m` - Slope, dimensionless.

If we know that
`(x_(1), y_(1)) = (0, 3)` and
`(x_(2), y_(2)) = (3, 0)`, the slope of both lines is:

`m = (0-3)/(3-0)`

`m = -1`

Any line is described by the following formula:

`y = m\cdot x + b`

Where:

`x` - Independent variable, dimensionless.

`y` - Dependent variable, dimensionless.

`m` - Slope, dimensionless.

`b` - y-Intercept, dimensionless.

The y-Intercept is cleared within the formula:

`b = y-m\cdot x`

Now we get the formula for each line depicted on figure:

a) The origin in figure a:
`(x, y) = (0, 0)`,
`m = -1`

`b = 0 - (-1) \cdot (0)`

`b = 0`

The formula for the figure A is
`y = -x`.

b) Point (0, 3) in figure b:
`(x, y) = (0, 3)`,
`m = -1`

`b = 3 - (-1)\cdot (0)`

`b = 3`

The formula for the figure B is
`y = -x +3`-